ALTERNATE CUBRENT GENERATOR. i 'J' 



For the purposes of the following discussioa we will assume that 

 when the magnetizing force — 



H = 7^ + A, + //.J + &c., 

 prod ces the induction — 



B = b, +h^ + b^ + &c., 

 then b, = fx^h,, J, = /xj/^, &c., where the /x,^s are operators of the type 

 given by /!„= »igt ~ "«• 



[This assumption as regards all the harmonics of B but the funda- 

 mental is not strictly in accordance with what is known concerning 

 the behaviour of laminated iron under periodic magnetizing forces, 

 for ^3, ij, &e., depend, at any rate for hirge values of 6, more on &, than 

 on A3, hi &c. At the same time it is hoped that the following discussion 

 may be of some value.] 



In general if H.-'^hg produce B = 'S,hg, as the total iron loss per 

 c.c. per cycle due to both hysteresis and eddy currents is — 



Where T is the period, the total iron loss per c.c. per second is — 



1 /7R 



= — . Average value of product H --- , 



1 . - 



= — ■ av. product ^liq into oa'^^q bq 



- Stt \ ^^^'^'' "^ ^ ^'^*^' "*" ^ ^'*5^-'+ *^- 1 (-See section 11.) 



= g- ^q If'hq sin 8,. 



Again, it is well knnwn that if the steady magnetizing current- 

 turn>* nx act on a magnetic circuit composed of different materials, the 

 flux E produced is given by — 



^ ^irnx 



"-TIL 



where the L,As are the lengths and sectional areas respectively of 

 the different portions of the circuit, and the /as are the permeabilities 

 of these portions for the particular flux densities in them. 



If now the magnetizing current be an alternating one, that is, if 

 X = x^ sin ((ut + c,) = a, (a vecior), the same equation will give the 

 corresponding harmonic of the flux produced, but the /xs are now the 

 permeability operators tor the diffiient portions of the circuit for the 

 amplitudes and period of the flux densities in them. 



2 j~ can, by the addition theorem in section 3, be reduced to a 

 single operator, so that if the flux /, (vector) be produced by the 



